Technological innovations have revolutionized the process of scientific research and knowledge discovery.  The availability of massive data and challenges from frontiers of research and development have reshaped statistical thinking, data analysis and theoretical studies.  The challenges of dimensionality arise from diverse fields of sciences and the humanities, ranging from computational biology and health studies to economics and finance. A comprehensive overview will be given on statistical challenges with vast dimensionality. The impact of dimensionality and spurious correlation will be addressed. What makes the high-dimensional problems feasible is the notion of sparisty. 
While the dimensionality can be much higher than the sample size, the intrinsic dimensionality is much smaller. A unified framework expoiting sparsity will be outlined.  Other related problems with vast-dimensionality are also discussed.